Re: a question on infinite models


"Bruce Samuels" <bsamuels@xxxxxxxxxx> wrote in message
news:c2Mje.27$XB2.77068@xxxxxxxxxxxxxxxxxxxxx
>
> "Chris Menzel" <cmenzel@xxxxxxxxxxxxxxxxxxxx> wrote in message
> news:slrnd8sprd.uu.cmenzel@xxxxxxxxxxxxxxxxxxxx
>> On Fri, 20 May 2005 15:32:00 GMT, Bruce Samuels <bsamuels@xxxxxxxxxx>
>> said:
>>> Can someone help me with this problem from Enderton chapter 2.6.8:
>>> Assume that phi is true in all infinite models of a theory T. Show that
>>> there is a finite mumber k such that phi is true in all models U of T
>>> for
>>> which |U| has k or more elements.
>>
>> Assume there is no such k -- formulate the denial carefully. You should
>> quickly see that it is inconsistent with an important corollary to the
>> completeness theorem.
>>
>
> Is there not also a proof that is a direct consequence of the
> Lowenheim-Skolem theorem?
>My apologies, I just learned that the Lowenheim_Skolem Theorem is
>considered a corallary of completeness.


.

Relevant Pages

  • Re: a question on infinite models
    ... >> Can someone help me with this problem from Enderton chapter 2.6.8: ... >> there is a finite mumber k such that phi is true in all models U of T for ... > completeness theorem. ...
    (sci.logic)
  • Re: a question on infinite models
    ... >>>Assume that phi is true in all infinite models of a theory T. Show ... >>>that there is a finite mumber k such that phi is true in all models U ... for some reason my university news server filtered Torkel's post -- I just ...
    (sci.logic)
  • Re: a question on infinite models
    ... > there is a finite mumber k such that phi is true in all models U of T for ... Prev by Date: ...
    (sci.logic)
  • Re: a question on infinite models
    ... >there is a finite mumber k such that phi is true in all models U of T for ... Prev by Date: ...
    (sci.logic)
  • Re: a question on infinite models
    ... >>Can someone help me with this problem from Enderton chapter 2.6.8: ... >>Assume that phi is true in all infinite models of a theory T. Show ... Prev by Date: ...
    (sci.logic)
Quantcast